In performing operations within a cased well, such as logging formation properties, it is important to know the exact location of the tool lowered into the well to perform the specific function. Measuring the depth of well logging tools is traditionally made from the surface, by measuring how much of the cable which supports the tools has been deployed. Both wireline tools and while-drilling tools rely on the same basic concept.
The depth of the tool string is commonly determined by passing the cable over a calibrated measurement wheel at the surface of the well. As the tool is deployed, the length of cable unspoiled into the well is monitored as an estimate of tool depth. Depth compensation for cable stretch may be attempted by calculating a theoretical stretch ration based upon cable length, elasticity and tool weight. Even with very elaborate compensation algorithms, however, the actual amount of cable stretching may vary over time and because of unforeseen and unmeasured interactions between the cable and tool string and the well bore (such as tool hang-ups and cable friction) and anomalies such as cable “bounce”. Deviated wells, in which the tool is pulled along the interior surface of the well casing, can present particular problems with variable and inconsistent cable loading, as the stool “sticks” and jumps along the well bore. Such problems are also encountered albeit to a lesser degree, in tubing-conveyed operations in which tubing length is measured by a wheel arranged to roll along the tubing as it is unspoiled. Even very small deployment length measurement error percentages and other discrepancies can result, with either type of deployment, in absolute tool positioning errors of several feet or more in a well of over a mile in depth, for example.
Another approach has been developed that measures the rotations of a set of calibrated wheels contacting the cable under a set force which generates enough friction to transmit any linear velocity of the cable to the perimeter of the wheels, allowing a direct measurement of the corresponding depth increment.
Yet another approach utilizes a pair of sensors located on or within the drill string along with a known reference point within the borehole. Given the distance between the two sensors is determined by the a relatively short piece of drill string, its stretch/compression effects are negligible compared to the stretch and compression observed on the total length of drill sting, and can be used as a downhole depth gauge by observing that when the second sensor will reach a correlable event already seen by the first sensor, the depth increment is the distance between the sensors.
Use of downhole sensors is challenging and present even more difficulties in the case of completed wells, in which the casing effects the ability to run certain downhole sensors. For example, steel casing has historically been thought of as a barrier to electromagnetic measurements of the properties of the formation. The problems presented by conductive liners are described by Augustin et al., in “A Theoretical Study of Surface-to-Borehole Electromagnetic Logging in Cased Holes,” Geophysics, Vol. 54, No. 1 (1989); Uchida et al., in “Effect of a Steel Casing on Crosshole EM Measurements,” SEG Annual Meeting, Texas (1991); and Wu et al., in “Influence of Steel Casing on Electromagnetic Signals,” Geophysics, Vol. 59, No. 3 (1994). These prior art references show that coupling between a transmitter and a conductive liner is independent of the surrounding geological formation conductivity for a wide range of practical formation resistivities encountered in the field and that the magnetic field produced inside the conductive liner at a distance of a few meters or less from the transmitter depends only on the conductive liner properties and not on the formation properties.
FIG. 1 shows typical equipment used in the measurement of geological formation 10 resistivity between two drill holes 12a and 12b using electromagnetic induction. A transmitter T is located in one borehole, while a receiver R is placed in another borehole. The transmitter T typically consists of a coil (not shown) having a multi-turn loop (which consists of NT turns of wire) wrapped around a magnetically permeable core (mu-metal, ferrite or other ferro-magnetic material) with a cross section, AT. The transmitter T may further comprise a capacitor (not shown) for tuning the frequency of the coil. When an alternating current, IT, at a frequency of f0 Hz passes through this multi-turn loop, a time varying magnetic moment, MT, is produced in the transmitter. This magnetic moment is defined as follows:MT=NTITAT  (1)The magnetic moment MT can be detected by the receiver R as a magnetic field, B0. The transmitter T, receiver R, or both are typically disposed in boreholes (e.g., 12a and 12b) in the earth formation 10. In this case, the detected magnetic field, B0, is proportional to the magnetic moment of the transmitter, MT, and to a geological factor, k1, as follows:B0=k1MT  (2)The geological factor, k1, is a function of the spatial location and orientation of a field component of the magnetic field, B0, with respect to the magnetic moment of the transmitter, MT.
The receiver R typically includes one or more antennas (not shown). Each antenna includes a multi-turn loop of wire wound around a core of magnetically permeable metal or ferrite. The changing magnetic field sensed by the receiver R creates an induced voltage in the receiver coil (not shown). This induced voltage (VR) is a function of the detected magnetic field (BR), the frequency (f0), the number of turns (NR) of wire in the receiver coil, the effective cross-sectional area of the coil (AR), and the effective permeability (ρR) of the coil. Thus, VR can be defined as follows:VR=πf0BRNRARρR  (3)While f0 and NR are known, the product, AR ρR, is difficult to calculate. In practice, these constants may be grouped together as kR and equation (3) may be simplified as:VR=kRBR  (4)where kR=πf0 NR AR ρR. Thus, instead of determining the product AR ρR, it is more convenient to determine kR according to the following procedures. First, the receiver coil is calibrated in a known field, at a known frequency. Then, the exact value for kR is derived from the magnetic field (BR) and the measured voltage (VR) according to the following equation:kR=BR/VR  (5)
When this system is placed in a conducting geological formation, the time-varying magnetic field, B0, which is produced by the transmitter magnetic moment, produces a voltage in the geological formation, which in turn drives a current therein, L1. The current, L1, is proportional to the conductivity of the geological formation and is generally concentric about the longitudinal axis of the borehole. The magnetic field proximate to the borehole results from a free space field, called the primary magnetic field, while the field resulting from current L1 is called the secondary magnetic field.
The current, L1, is typically out of phase with respect to the transmitter current, IT. At very low frequencies, where the inductive reactance is small, the current, L1, is proportional to dB/dt and is 90° out of phase with respect to IT. As the frequency increases, the inductive reactance increases and the phase of the induced current, L1, increases to be greater than 90°. The secondary magnetic field induced by current L1 also has a phase shift relative to the induced current L1 and so the total magnetic field as detected by receiver R is complex.
The complex magnetic field detected by receiver R may be separated into two components: a real component, IR, which is in-phase with the transmitter current, IT, and an imaginary (or quadrature) component, II, which is phase-shifted by 90°. The values of the real component, IR, and the quadrature component, II, of the magnetic field at a given frequency and geometrical configuration uniquely specify the electrical resistivity of a homogeneous formation pierced by the drill holes. In an inhomogeneous geological formation, however, the complex field is measured at a succession of points along the longitudinal axis of the receiver borehole for each of a succession of transmitter locations. The multiplicity of measurements thus obtained can then be used to determine the inhomogeneous resistivity between the holes.
In both cases, i.e., measuring homogeneous geological formation resistivity or measuring inhomogeneous geological formation resistivity, the measurements are typically made before extraction of hydrocarbons takes place. This is because the boreholes typically are cased with conductive liners (e.g., metallic casing; see 16a and 16b in FIG. 3) in order to preserve the physical integrity of the borehole during hydrocarbon extraction. The conductive tubular liners interfere with resistivity measurements and are difficult and costly to remove from the borehole once they are installed. As a result, prior art systems such as that shown in FIG. 1 are not suitable for analyzing hydrocarbon reservoirs once extraction of the hydrocarbons begins.
The net or effective moment, Meff, of a transmitter inside a conductive liner is dictated by the inductive coupling between the transmitter and the conductive liner. Physically, the resistivity of the conductive liner is very low and the inductance relatively high. This property results in a current of almost the same magnitude as that of the transmitter current being induced in the conductive liner. Lenz's Law predicts that the magnetic field generated by this induced current in the conductive liner will oppose the time-varying magnetic field produced by the transmitter current. Thus, the magnetic field generated by the transmitter is mostly cancelled out by the magnetic field generated by the conductive liner. As a result, the magnetic field external to the conductive liner is greatly reduced, and its magnitude is proportional to the difference in currents in the transmitter and the conductive liner. In effect, the conductive liner “shields” the transmitter from any receiver positioned outside of the conductive liner.
An analogous situation is present with respect to a receiver if it is surrounded by a conductive liner. The field to be detected induces currents concentric with the receiver coil whose sense is such as to reduce the field within the liner. The field to be detected is consequently highly attenuated and the measurement is highly influenced by the variations in attenuation caused by the variation in liner properties, and example of which is graphically demonstrated by the slope of curve 10 shown in FIG. 2. The situation is exacerbated if both the transmitter and the receiver are surrounded by conductive liners. Often the design criteria for a crosshole survey of a cased borehole reduces the signal to a level that is undetectable by standard receivers. Moreover, the variance in conductivity, permeability, and thickness along a longitudinal axis of a liner makes difficult determining the attenuation factor at any given point.
The attenuation due to a steel casing surrounding the transmitter for a homogeneous formation is essentially constant a few meters form the source. Since the attenuation is constant the ratio of the fields as described, and incorporated herein, in U.S. Pat. No. 6,294,917 B1, to Nichols, removes the effects of the casing. This constancy of the fields can also be removed by calculating a shift operator as described, and incorporated herein, in U.S. Pat. No. 6,393,363 B1 to Wilt and Nichols. However, for multiple cased boreholes, both the ratio and shift operator methods preferably utilize an extra monitor for the transmitted field.